Intermediate Macroeconomics

Julio Gaŕın

Claremont McKenna College

Robert Lester

Colby College

Eric Sims

University of Notre Dame

September 23, 2020

This Version: 3.0.0

This is a book designed for use in an intermediate macroeconomics course or a masters

level course in macroeconomics. It could also be used by graduate students seeking a refresher

in advanced undergraduate macroeconomics. This book represents a substantial makeover

and extension of the course notes for intermediate macroeconomics which have been provided

publicly on Eric Sims’s personal website for several years.

There are many fine textbooks for macroeconomics at the intermediate level currently

available. These texts include, but are certainly not limited to, Mankiw (2016), Williamson

(2014), Jones (2013), Barro (1997), Abel, Bernanke, and Croushore (2017), Gordon (2012),

Hall and Pappell (2005), Blanchard (2017), Dornbusch, Fischer, and Startz (2013), Froyen

(2013), and Chugh (2015).

Given the large number of high quality texts already on the market, why the need for

a new one? We view our book as fulfilling a couple of important and largely unmet needs

in the existing market. First, our text makes much more use of mathematics than most

intermediate books. Second, whereas most textbooks divide the study of the macroeconomy

into two “runs” (the long run and the short run), we focus on three runs – the long run, the

medium run, and the short run. Third, we have attempted to emphasize the microeconomic

underpinnings of modern macroeconomics, all the while maintaining tractability and a focus

on policy. Fourth, we include a section on banking, bank runs, bond pricing, and the stock

market. While this material is generally left to money, credit, and banking texts, the recent

Great Recession has taught us the importance of thinking seriously about the implications

of the financial system for the macroeconomy. Finally, we feel that a defining feature of

this text is that it is, if nothing else, thorough – we have tried hard to be very clear about

mathematical derivations and to not skip steps when doing them.

Modern economics is increasingly quantitative and makes use of math. While it is

important to emphasize that math is only a tool deployed to understand real-world phenomena,

it is a highly useful tool. Math clearly communicates ideas which are often obfuscated when

only words are used. Math also lends itself nicely to quantitative comparisons of models

with real-world data. Our textbook freely makes use of mathematics, more so than most

of the texts we cited above. An exception is Chugh (2015), who uses more math than we

do. To successfully navigate this book, a student needs to be proficient at high school level

algebra and be comfortable with a couple of basic rules of calculus and statistics. We have

included Appendices A and B to help students navigate the mathematical concepts which

are used throughout the book. While we find the approach of freely integrating mathematics

into the analysis attractive, we recognize that it may not be well-suited for all students and

all instructors. We have therefore written the book where the more involved mathematical

analysis is contained in Part III. This material can be skipped at the instructor’s discretion,

1

http://www3.nd.edu/~esims1/

which allows an instructor to spend more time on the more graphical analysis used in Parts

IV and V.

Traditionally, macroeconomic analysis is divided into the “long run” (growth) and the

“short run” (business cycles). We have added a third run to the mix, which we call the

“medium run.” This is similar to the approach in Blanchard (2017), although we reverse

ordering relative to Blanchard, studying the long run first, then the medium run, then the

short run. Our principal framework for studying the long run in Part II is the canonical Solow

model. We are attracted to this framework because it clearly elucidates the important role of

productivity in accounting for both long run growth and cross-country income differences. A

drawback is that the Solow model does not formally model microeconomic decision-making,

as we do throughout the rest of the book. To that end, we have also included Chapter 8

using an overlapping generations framework with optimizing agents. This framework touches

on many of the same issues as the Solow model, but allows us to address a number of other

issues related to efficiency and the role of a government.

Whereas growth theory studies the role of capital accumulation and productivity growth

over the span of decades, we think of the medium run as focusing on frequencies of time

measured in periods of several years. Over this time horizon, investment is an important

component of fluctuations in output, but it is appropriate to treat the stock of physical

capital as approximately fixed. Further, nominal frictions which might distort the short run

equilibrium relative to an efficient outcome are likely not relevant over this time horizon.

Our framework for studying the medium run is what we call the neoclassical model (or real

business cycle model). In this framework, output is supply determined and the equilibrium is

efficient. The microeconomic underpinnings of the neoclassical model are laid out in Part III

and a full graphical treatment is given in Part IV.

We think of the short run as focusing on periods of time spanning months to several years.

Our framework for studying the short run is a New Keynesian model with sticky prices. This

analysis is carried out in Part V. The only difference between our medium and short run

models is the assumption of price rigidity, which makes the AS curve non-vertical – otherwise

the models are the same. We consider two different versions of the sticky price model – one

in which the price level is completely predetermined within period (the simple sticky price

model) and another in which the price level is sensitive to the output gap (the partial sticky

price model). With either form of price stickiness, demand shocks matter, and the scope for

beneficial short run monetary and/or fiscal policies becomes apparent. Optimal monetary

policy and complications raised by the zero lower bound (ZLB) are addressed. Appendix D

develops a sticky wage model which has similar implications to the sticky price model.

Modern macroeconomics is simply microeconomics applied at a high level of aggregation.

2

To that end, we have devoted an entire part of the book, Part III, to the “Microeconomics of

Macroeconomics.” There we study an optimal consumption-saving problem, a firm profit

maximization problem in a dynamic setting, equilibrium in an endowment economy, and

discuss fiscal policy, money, and the First Welfare Theorem. Whereas for the most part we

ignore unemployment throughout the book and instead simply focus on total labor input, we

also include a chapter on search, matching, and unemployment. The analysis carried out in

Part III serves as the underpinning for the remainder of the medium and short run analysis

in the book, but we have tried to write the book where an instructor can omit Part III should

he or she choose to do so.

Relatedly, modern macroeconomics takes dynamics seriously. We were initially attracted

to the two period macroeconomic framework used in Williamson (2014), for which Barro

(1997) served as a precursor. We have adopted this two period framework for Parts III through

V. That said, our experience suggested that the intertemporal supply relationship (due to

an effect of the real interest rate on labor supply) that is the hallmark of the Williamson

(2014) approach was ultimately confusing to students. It required spending too much time

on a baseline market-clearing model of the business cycle and prevented moving more quickly

to a framework where important policy implications could be addressed. We have simplified

this by assuming that labor supply does not depend on the real interest rate. This can be

motivated formally via use of preferences proposed in Greenwood, Hercowitz, and Huffman

(1988), which feature no wealth effect on labor supply.

We were also attracted to the timeless IS-LM approach as laid out, for example, so

eloquently by Mankiw (2016), Abel, Bernanke, and Croushore (2017), and others. Part V

studies a short run New Keynesian model, freely making use of the commonly deployed

IS-LM-AD-AS analysis. The medium run model we develop graphically in part IV can be

cast in this framework with a vertical AS curve, which is often called the “long run supply

curve” (or LRAS) in some texts. Because of our simplification concerning the dynamic nature

of labor supply in Part IV, we can move to the short run analysis in Part V quicker. Also,

because the medium run equilibrium is efficient and the medium run can be understood as a

special case of the short run, the policy implications in the short run become immediately

clear. In particular, policy should be deployed in such a way that the short run equilibrium

(where prices are sticky) coincides with the medium run equilibrium. Price stability is often

a good normative goal, and monetary policy ought to target the natural or neutral rate

of interest, which is the interest rate which would obtain in the absence of price or wage

rigidities. This “Wicksellian” framework for thinking about policy is now the dominant

paradigm for thinking about short run fluctuations in central banks. Within the context of

the IS-LM-AD-AS model, we study the zero lower bound and an open economy version of

3

the model. Jones (2013) proposes replacing the LM curve with the monetary policy (MP)

curve, which is based on a Taylor rule type framework for setting interest rates. We include

an appendix, Appendix E, where the MP curve replaces the LM curve.

Finally, the recent Great Recession has highlighted the importance of thinking about

connections between the financial system and the macroeconomy. Part VI of the book is

dedicated to studying banking, financial intermediation, and asset pricing in more depth. We

include chapters on the basics of banking and bank runs, as well as a chapter that delves into

the money supply process in more detail. We also have detailed chapters on bond and stock

pricing in a dynamic, optimizing framework based on the stochastic discount factor. Much of

this material is traditionally reserved for money, credit, and banking courses, but we think

that recent events make the material all the more relevant for conventional macroeconomics

courses. Chapter 36 incorporates an exogenous credit spread variable into our medium/short

run modeling framework and argues that exogenous increases in credit spreads are a sensible

way to model financial frictions and crises. Chapter 37 provides an in-depth accounting of the

recent financial crisis and Great Recession and deploys the tools developed elsewhere in the

book to understand the recession and the myriad policy interventions undertaken in its wake.

In writing this book, we have tried to follow the lead of Glenmorangie, the distillery

marketing itself as producing Scotch that is “unnecessarily well-made.” In particular, we

have attempted throughout the book to be unnecessarily thorough. We present all the steps

for various mathematical derivations and go out of our way to work through all the steps

when deriving graphs and shifting curves. This all makes the book rather than longer than

it might otherwise be. In a sense, it is our hope that a student could learn from this text

without the aid of a formal instructor, though we think this is suboptimal. Our preference

for this approach is rooted in our own experiences as students, where we found ourselves

frustrated (and often confused) when instructors or textbooks skipped over too many details,

instead preferring to focus on the “big picture.” There is no free lunch in economics, and

our approach is not without cost. At present, the book is short on examples and real-world

applications. We hope to augment the book along these dimensions in the coming months

and years. The best real world examples are constantly changing, and this is an area where

the instructor contributes some value added, helping to bring the text material to life.

The book is divided into six main parts. Part I serves as an introduction. Chapter 1

reviews some basic definitions of aggregate macroeconomic variables. While most students

should have seen this material in a principles course, we think it is important for them to

see it again. Chapter 2 defines what an economic model is and why a model is useful. This

chapter motivates the rest of the analysis in the book, which is based on models. Chapter 3

provides a brief overview of the history and controversies of macroeconomics.

4

https://www.glenmorangie.com/en-us/

We study the long run in Part II. We put the long run first, rather than last as in many

textbooks, for two main reasons. First, growth is arguably much more important for welfare

than is the business cycle. As Nobel Prize winner Robert Lucas once famously said, “Once you

start to think about growth, it is difficult to think about anything else.” Second, the standard

Solow model for thinking about growth is not based on intertemporal optimization, but

rather assumes a constant saving rate. This framework does not fit well with the remainder

of the book, which is built around intertemporal optimization. Nevertheless, the Solow model

delivers many important insights about both the long run trends of an economy and the

sizeable cross-country differences in economic outcomes. Chapter 4 lays out some basic

facts about economic growth based on the contribution of Kaldor (1957). Chapter 5 studies

the textbook Solow model. Chapter 6 considers an augmented version of the Solow model

with exogenous productivity and population growth. Chapter 7 uses the Solow model to

seek to understand cross-country differences in income. In the most recent edition of the

book, we have also included a chapter using a dynamic, optimizing, overlapping generations

framework (Chapter 8). While touching on similar issues to the Solow model, it allows to

discuss things like market efficiency and potentially beneficial roles of a government. Though

it ends up having similar implications as the Solow model, because the OLG economy features

optimizing households in the context of a growth model, it provides a nice bridge to later

parts of the book.

Part III is called the “Microeconomics of Macroeconomics” and studies optimal decision

making in a two period, intertemporal framework. This is the most math-heavy component

of the book, and later parts of the book, while referencing the material from this part, are

meant to be self-contained. Chapter 9 studies optimal consumption-saving decisions in a

two period framework, making use of indifference curves and budget lines. It also considers

several extensions to the two period framework, including a study of the roles of wealth,

uncertainty, and liquidity constraints in consumption-saving decisions. Chapter 10 extends

this framework to more than two periods. Chapter 11 introduces the concept of competitive

equilibrium in the context of the two period consumption-saving framework, emphasizing that

the real interest rate is an intertemporal price which adjusts to clear markets in equilibrium.

It also includes some discussion on heterogeneity and risk-sharing, which motivates the use

of the representative agent framework used throughout the book. Chapter 12 introduces

production, and studies optimal labor and investment demand for a firm and optimal labor

supply for a household. Chapter 13 introduces fiscal policy into this framework. Here we

discuss Ricardian Equivalence, which is used later in the book, but also note the conditions

under which Ricardian Equivalence will fail to hold. Chapter 14 introduces money into

the framework, motivating the demand for money through a money in the utility function

5

https://en.wikipedia.org/wiki/Robert_Lucas_Jr.

assumption. Here we do not go into detail on the money creation process, instead reserving

that material for later in the book (Chapter 32). Chapter 15 discusses the equivalence of the

dynamic production economy model laid out in Chapter 12 to the solution to a social planner’s

problem under certain conditions. In the process we discuss the First Welfare Theorem.

Although we are mostly silent on unemployment, Chapter 17 includes a microeconomically

founded discussion of unemployment using the Diamond-Mortensen-Pissarides framework.

The medium run is studied in Part IV. We refer to our model for understanding the medium

run as the neoclassical model. It is based on the intertemporal frictionless production economy

studied in more depth in Chapter 12, though the material is presented in such a way as to be

self-contained. Most of the analysis is graphical in nature. The consumption, investment,

money, and labor demand schedules used in this part come from the microeconomic decision-

making problems studied in Part III, as does the labor supply schedule. Chapter 18 discusses

these decision rules and presents a graphical depiction of the equilibrium, which is based on a

traditional IS curve summarizing the demand side and a vertical curve which we will the Y s

curve (after Williamson 2014) to describe the supply-side. The Y s curve is vertical, rather

than upward-sloping in a graph with the real interest rate on the vertical axis and output on

the horizontal, because of our assumption of no wealth effects on labor supply. Appendix

C carries out the analysis where the Y s curve is instead upward-sloping, as in Williamson

(2014). Chapter 19 graphically works through the effects of changes in exogenous variables on

the endogenous variables of the model. Chapter 20 presents some basic facts about observed

business cycle fluctuations and assesses the extent to which the neoclassical model can provide

a reasonable account of those facts. In Chapter 21 we study the connection between the

money supply, inflation, and nominal interest rates in the context of the neoclassical model.

Chapter 22 discusses the policy implications of the model. The equilibrium is efficient, and

so there is no scope for policy to attempt to combat fluctuations with monetary or fiscal

interventions. In this chapter we also include an extensive discussion of criticisms which have

been levied at the neoclassical / real business cycle paradigm for thinking about economic

policy. Chapter 23 considers an open economy version of the neoclassical model, studying

net exports and exchange rates.

Part V studies a New Keynesian model. This model is identical to the neoclassical

model, with the exception that the aggregate price level is sticky. This stickiness allows

demand shocks to matter and means that money is non-neutral. It also means that the short

run equilibrium is in general inefficient, opening the door for desirable policy interventions.

Chapter 24 develops the IS-LM-AD curves to describe the demand side of the model. What

differentiates the New Keynesian model from the neoclassical model is not the demand side,

but rather the supply side. Hence, the IS-LM-AD curves can also be used to describe the

6

demand side of the neoclassical model. We prefer our approach of first starting with the IS-Y s

curves because it better highlights monetary neutrality and the classical dichotomy. Chapter

25 develops a theory of a non-vertical aggregate supply curve based on price stickiness.

An appendix develops a New Keynesian model based on wage stickiness rather than price

stickiness, Appendix D. Chapter 26 works out the effects of changes in exogenous variables

on the endogenous variables of the New Keynesian model and compares those effects to

the neoclassical model. Chapter 27 develops a theory of the transition from short run to

medium run. In particular, if the short run equilibrium differs from what would obtain

in the neoclassical model, over time pressure on the price level results in shifts of the AS

relationship that eventually restore the neoclassical equilibrium. On this basis we provide

theoretical support for empirically observed Phillips Curve relationships. In Chapter 28 we

study optimal monetary policy in the Keynesian model. The optimal policy is to adjust the

money supply / interest rates so as to ensure that the equilibrium of the short run model

coincides with the equilibrium which would obtain in the absence of price rigidity (i.e. the

neoclassical, medium run equilibrium). Here, we talk about the Wicksellian “natural” or

“neutral” rate of interest and its importance for policy. We also discuss the benefits of price

stability. Chapter 29 studies the New Keynesian model when the zero lower bound is binding.

Chapter 30 considers an open economy version of the New Keynesian model.

Recent events have highlighted the important connection between finance and macroe-

conomics. Part VI is dedicated to these issues. Chapter 31 discusses the basic business

of banking and focuses on bank balance sheets. There we also discuss how banking has

changed in the last several decades, discussing the rise of a so-called “shadow banking” sector.

Chapter 32 studies the creation of money and defines terms like the monetary base and

the money multiplier. Chapter 33 discusses the usefulness of the liquidity transformation

in which financial intermediaries engage and the sensitivity of financial intermediaries to

runs. To that end, we provide a simplified exposition of the classic Diamond and Dybvig

(1983) model of bank runs. This material proves useful in thinking about the recent financial

crisis. Chapters 34 and 35 study asset pricing in the context of a microeconomically founded

consumption capital asset pricing model (CAPM) based on the stochastic discount factor.

Chapter 34 studies the risk and term structures of interest rates and provides a framework

for thinking seriously about both conventional and unconventional monetary policy. Chapter

35 studies the stock market and seeks to understand the equity premium. We also discuss

the possibility of bubbles and whether policy ought to try to prevent them.

Although much research has been recently done, it is not straightforward to incorporate a

non-trivial financial system in a compelling and tractable way into an otherwise standard

macroeconomic framework. In Chapter 36, we argue that a convenient short cut is to include

7

an exogenous credit spread variable which we label ft. This spread represents a premium

firms must pay to finance investment over the return households receive on saving. It serves

as a convenient stand-in for both the risk and term structures of interest rates. We argue

that financial crises are best characterized as runs on liquidity which result in large increases

in credit spreads. In terms of the IS-LM-AD-AS model, an increase in the exogenous credit

spread variable shifts the IS and AD curves in to the left. In Chapter 37 we study financial

crises more generally with a particular focus on the recent Great Recession. The presentation

of this chapter ought to be at least somewhat self-contained, but it does make use of concepts

studied in detail in Parts V and VI. We present facts, talk about the conventional wisdom

concerning the origins of the crisis, map those origins into our New Keynesian framework,

and then use that framework to think about the myriad unconventional policy measures

which were deployed.

We realize that there is likely too much material presented here for a normal one semester

course. It is our hope that our approach of presenting the material in as thorough as possible

a manner will facilitate moving through the material quickly. As alluded to above, there are

a number of different ways in which this book can be used. Part I could be skipped entirely,

an instructor could have a teaching assistant work through it, or an instructor could require

students to read the material on their own without devoting scarce class time to it. For

studying growth, it may suffice to only focus on Chapter 5, skipping the augmented Solow

model with exogenous productivity and population growth and/or the chapter on overlapping

generations. Chapter 7 is written in such a way that the material in Chapter 6 need not have

previously been covered.

Some instructors may see fit to skip all or parts of Part III. One option for condensing

this material would be to skip Chapters 10 (which considers a multi-period extension of

the two period consumption-saving model), 11 (which studies equilibrium in an endowment

economy), or parts of Chapters 14 through 15. In Parts IV and V, one can condense the

material by skipping the open economy chapters, Chapters 23 and 30. The book can be

taught without any reference at all to the material in Part VI. Some instructors may find it

suitable to substitute this material for other chapters. As this book is a work in progress, we

too are experimenting with how to best structure a course based on this book, and would

appreciate any feedback from instructors who have tried different course structures elsewhere.

Throughout the book, we include hyperlinked references to academic papers and other

readings. These are denoted in blue and appear in the format “Name (year of publication).”

For many publications, the references section includes hyperlinks to the papers in question.

We also include hyperlinks to other external readings, in many cases Wikipedia entries

on topics of interest. These are also indicated in blue, and in the online version can be

8

https://www.wikipedia.org/

navigated to with a simple click. At the conclusion of each chapter, we include two sets of

problems – one is called “Questions for Review” and requires mostly short written responses

which simply review the material presented in the text, while the other is called “Exercises”

and typically features longer problems requiring students to work through mathematical or

graphical derivations, often times including extensions of the models presented in the text.

Modern macroeconomics is quantitative, and quantitative skills are increasingly valued in

many different types of jobs. To that end, we include several questions which require the

students to work with data (either actual or artificial) using Microsoft Excel. These are

demarcated with the indicator “[Excel problem]”.

We are grateful to several generations of undergraduate students at the University of

Notre Dame, the University of Georgia, Claremtont McKenna College, and Colby College

who have taken intermediate macro courses using early versions of the course notes which

eventually grew into this book. Their comments and feedback have improved the presentation

and content of the resulting material. Ultimately, our students – past and future ones – are

the reason we wrote this text. We are also grateful to Michael Pries for extensive comments

on an earlier draft of this book.

We welcome any feedback on the textbook. As it is a work in progress, the manuscript is

almost surely littered with typos and sections that may not be perfectly clear. If you have

comments or suggestions along any of these lines, please email them to us at the addresses

given below.

Julio Gaŕın

Claremont McKenna College

jgarin@cmc.edu

Robert Lester

Colby College

rblester@colby.edu

Eric Sims

University of Notre Dame

esims1@nd.edu

9

mailto:jgarin@uga.edumailto:rblester@colby.edumailto:esims1@nd.edu

Contents

I Introduction 21

1 Macroeconomic Data 23

1.1 Calculating GDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

1.2 Real versus Nominal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

1.3 The Consumer Price Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

1.4 Measuring the Labor Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2 What is a Model? 45

2.1 Models and Why Economists Use Them . . . . . . . . . . . . . . . . . . . . . . . 45

2.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3 Brief History of Macroeconomic Thought 49

3.1 The Early Period: 1936-1968 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.2 Blowing Everything Up: 1968-1981 . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.3 Modern Macroeconomics: 1982-2016 . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

II The Long Run 55

4 Facts About Economic Growth 57

4.1 Economic Growth over Time: The Kaldor Facts . . . . . . . . . . . . . . . . . . 57

4.2 Cross Country Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5 The Basic Solow Model 72

5.1 Production, Consumption, and Investment . . . . . . . . . . . . . . . . . . . . . 72

5.2 Graphical Analysis of the Solow Model . . . . . . . . . . . . . . . . . . . . . . . . 81

5.3 The Algebra of the Steady State with Cobb-Douglas Production . . . . . . . . 88

10

5.4 Experiments: Changes in s and A . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.5 The Golden Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6 The Augmented Solow Model 107

6.1 Introducing Productivity and Population Growth . . . . . . . . . . . . . . . . . 107

6.2 Graphical Analysis of the Augmented Model . . . . . . . . . . . . . . . . . . . . 112

6.3 The Steady State of the Augmented Model . . . . . . . . . . . . . . . . . . . . . 113

6.4 Experiments: Changes in s and A . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

6.5 The Golden Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

6.6 Will Economic Growth Continue Indefinitely? . . . . . . . . . . . . . . . . . . . 128

6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

7 Understanding Cross-Country Income Differences 132

7.1 Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

7.1.1 Conditional Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

7.2 Can Differences in s Account for Large Per Capita Output Differences? . . . . 139

7.3 The Role of Productivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

8 Overlapping Generations 149

8.1 The General Overlapping Generations Model . . . . . . . . . . . . . . . . . . . . 149

8.1.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

8.1.2 Firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

8.1.3 Equilibrium and Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . 153

8.2 Cobb-Douglas Production and Logarithmic Utility . . . . . . . . . . . . . . . . . 157

8.3 The Golden Rule and Dynamic Inefficiency . . . . . . . . . . . . . . . . . . . . . 162

8.3.1 Government Intervention . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

8.4 Incorporating Exogenous Technological Growth . . . . . . . . . . . . . . . . . . 171

8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

III The Microeconomics of Macroeconomics 178

9 A Dynamic Consumption-Saving Model 180

9.1 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

9.2 Optimization and the Euler Equation . . . . . . . . . . . . . . . . . . . . . . . . 185

9.3 Indifference Curve / Budget Line Analysis and the Consumption Function . . 188

11

9.4 Extensions of the Two Period Consumption-Saving Model . . . . . . . . . . . . 201

9.4.1 Wealth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

9.4.2 Permanent and Transitory Income Changes . . . . . . . . . . . . . . . . 205

9.4.3 Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

9.4.4 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

9.4.5 Consumption and Predictable Changes in Income . . . . . . . . . . . . . 214

9.4.6 Borrowing Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

9.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

10 A Multi-Period Consumption-Saving Model 228

10.1 Multi-Period Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

10.2 The MPC and Permanent vs. Transitory Changes in Income . . . . . . . . . . 235

10.3 The Life Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

10.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

11 Equilibrium in an Endowment Economy 247

11.1 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

11.2 Competitive Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

11.3 Identical Agents and Graphical Analysis of the Equilibrium . . . . . . . . . . . 249

11.3.1 Supply Shock: Increase in Yt . . . . . . . . . . . . . . . . . . . . . . . . . 256

11.3.2 Demand Shock: Increase in Yt+1 . . . . . . . . . . . . . . . . . . . . . . . 258

11.3.3 An Algebraic Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

11.4 Agents with Different Endowments . . . . . . . . . . . . . . . . . . . . . . . . . . 261

11.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

12 Production, Labor Demand, Investment, and Labor Supply 270

12.1 Firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

12.1.1 Diversion on Debt vs. Equity Finance . . . . . . . . . . . . . . . . . . . . 277

12.2 Household . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

12.3 Financial Intermediary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

12.4 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

12.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

13 Fiscal Policy 294

13.1 The Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

13.2 Fiscal Policy in an Endowment Economy . . . . . . . . . . . . . . . . . . . . . . 295

13.2.1 Graphical Effects of Changes in Gt and Gt+1 . . . . . . . . . . . . . . . . 299

12

13.2.2 Algebraic Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

13.3 Fiscal Policy in a Production Economy . . . . . . . . . . . . . . . . . . . . . . . . 303

13.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

14 Money 312

14.1 What is Money? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312

14.2 Modeling Money in our Production Economy . . . . . . . . . . . . . . . . . . . . 315

14.2.1 Household . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316

14.2.2 Firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

14.2.3 Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

14.2.4 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

14.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

15 Equilibrium Efficiency 333

15.1 The Social Planner’s Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334

15.1.1 The Basic Planner’s Problem . . . . . . . . . . . . . . . . . . . . . . . . . 335

15.1.2 Planner Gets to Choose Mt . . . . . . . . . . . . . . . . . . . . . . . . . . 338

15.1.3 Planner Gets to Choose Gt and Gt+1 . . . . . . . . . . . . . . . . . . . . . 340

15.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342

16 Monopolistic Competition 346

16.1 The Microeconomics of Monopoly . . . . . . . . . . . . . . . . . . . . . . . . . . . 346

16.2 A General Equilibrium Model of Monopolistic Competition . . . . . . . . . . . 349

16.2.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

16.2.2 Production Part I: The Product Bundler . . . . . . . . . . . . . . . . . . 350

16.2.3 Production Part II: Intermediate Good Firms . . . . . . . . . . . . . . . 352

16.2.4 Aggregation and Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . 354

16.2.5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

16.2.6 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

16.3 Markups and Labor’s Share of Income . . . . . . . . . . . . . . . . . . . . . . . . 358

16.4 Endogenous Entry and the Gains to Variety . . . . . . . . . . . . . . . . . . . . 360

16.4.1 Free Entry Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

16.4.2 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364

16.5 Firm Dynamics: Theory and Evidence . . . . . . . . . . . . . . . . . . . . . . . . 366

16.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367

13

17 Search, Matching, and Unemployment 369

17.1 Stylized Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370

17.2 One-Sided Search: The McCall Model . . . . . . . . . . . . . . . . . . . . . . . . 374

17.2.1 Probability: A Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

17.2.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

17.2.3 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377

17.2.4 Example: Uniform Distribution . . . . . . . . . . . . . . . . . . . . . . . . 379

17.3 The Bathtub Model of Unemployment . . . . . . . . . . . . . . . . . . . . . . . . 381

17.3.1 Transition Dynamics: A Quantitative Experiment . . . . . . . . . . . . . 383

17.4 Two Sided Matching: The Diamond-Mortensen-Pissarides Model . . . . . . . . 386

17.4.1 The Matching Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386

17.4.2 Household and Firm Behavior . . . . . . . . . . . . . . . . . . . . . . . . . 388

17.4.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

17.4.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392

17.4.5 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

17.5 Wage Posting and Directed Search . . . . . . . . . . . . . . . . . . . . . . . . . . 395

17.5.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397

17.5.2 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

17.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400

IV The Medium Run 404

18 The Neoclassical Model 406

18.1 Household . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406

18.2 Firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409

18.3 Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411

18.4 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412

18.5 Graphing the Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

18.5.1 The Demand Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

18.5.2 The Supply Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

18.5.3 Bringing it all Together . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419

18.5.4 The Nominal Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421

18.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423

19 Effects of Shocks in the Neoclassical Model 426

19.1 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426

14

19.2 The Effects of Changes in Exogenous Variables on the Endogenous Variables . 428

19.2.1 Productivity Shock: Increase in At: . . . . . . . . . . . . . . . . . . . . . 429

19.2.2 Expected Future Productivity Shock: Increase in At+1 . . . . . . . . . . 431

19.2.3 Government Spending Shock: Increase in Gt: . . . . . . . . . . . . . . . 434

19.2.4 An Increase in the Money Supply: Increase in Mt . . . . . . . . . . . . . 441

19.2.5 Expected Future Inflation: Increase in πet+1 . . . . . . . . . . . . . . . . . 442

19.2.6 Summary of Qualitative Effects . . . . . . . . . . . . . . . . . . . . . . . . 443

19.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

20 Taking the Neoclassical Model to the Data 448

20.1 Measuring the Business Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

20.2 Can the Neoclassical Model Match Business Cycle Facts? . . . . . . . . . . . . 451

20.3 Is there Evidence that At Moves Around in the Data? . . . . . . . . . . . . . . 454

20.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457

21 Money, Inflation, and Interest Rates 460

21.1 Measuring the Quantity of Money . . . . . . . . . . . . . . . . . . . . . . . . . . . 460

21.1.1 How is the Money Supply Set? . . . . . . . . . . . . . . . . . . . . . . . . 462

21.2 Money, the Price Level, and Inflation . . . . . . . . . . . . . . . . . . . . . . . . . 466

21.3 Inflation and Nominal Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . 472

21.4 The Money Supply and Real Variables . . . . . . . . . . . . . . . . . . . . . . . . 474

21.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477

22 Policy Implications and Criticisms of the Neoclassical Model 481

22.1 Criticisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481

22.1.1 Measurement of TFP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482

22.1.2 What are these Productivity Shocks? . . . . . . . . . . . . . . . . . . . . 484

22.1.3 Other Quantitative Considerations . . . . . . . . . . . . . . . . . . . . . . 484

22.1.4 An Idealized Description of the Labor Market . . . . . . . . . . . . . . . 484

22.1.5 Monetary Neutrality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485

22.1.6 The Role of Other Demand Shocks . . . . . . . . . . . . . . . . . . . . . . 485

22.1.7 Perfect Financial Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

22.1.8 An Absence of Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . 487

22.2 A Defense of the Neoclassical Model . . . . . . . . . . . . . . . . . . . . . . . . . 487

22.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

15

23 Open Economy Version of the Neoclassical Model 490

23.1 Exports, Imports, and Exchange Rates . . . . . . . . . . . . . . . . . . . . . . . . 490

23.2 Graphically Characterizing the Equilibrium . . . . . . . . . . . . . . . . . . . . . 495

23.3 Effects of Shocks in the Open Economy Model . . . . . . . . . . . . . . . . . . . 503

23.3.1 Positive IS Shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503

23.3.2 Increase in At . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507

23.3.3 Increase in Qt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510

23.3.4 Increase in Mt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

23.3.5 Increase in P Ft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

23.3.6 Summary of Qualitative Effects . . . . . . . . . . . . . . . . . . . . . . . . 513

23.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514

V The Short Run 517

24 The New Keynesian Demand Side: IS-LM-AD 521

24.1 The LM Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522

24.2 The IS Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525

24.3 The AD Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527

24.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531

25 The New Keynesian Supply Side 534

25.1 The Neoclassical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534

25.2 New Keynesian Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539

25.2.1 Simple Sticky Price Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 539

25.2.2 Partial Sticky Price Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 543

25.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552

26 Effect of Shocks in the New Keynesian Model 554

26.1 The Neoclassical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554

26.2 Simple Sticky Price Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561

26.3 Partial Sticky Price Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571

26.4 Comparing the New Keynesian Model to the Neoclassical Model . . . . . . . . 583

26.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585

27 Dynamics in the New Keynesian Model: Transition from Short Run to

Medium Run 588

27.1 Simple Sticky Price Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589

16

27.1.1 A Non-Optimal Short Run Equilibrium . . . . . . . . . . . . . . . . . . . 589

27.1.2 Dynamic Responses to Shocks . . . . . . . . . . . . . . . . . . . . . . . . . 592

27.2 Partial Sticky Price Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600

27.2.1 A Non-Optimal Short Run Equilibrium . . . . . . . . . . . . . . . . . . . 600

27.2.2 Dynamic Responses to Shocks . . . . . . . . . . . . . . . . . . . . . . . . . 603

27.3 The Phillips Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612

27.3.1 Implications of the Phillips Curve for Monetary Policy . . . . . . . . . . 616

27.3.2 The Possibility of Costless Disinflation . . . . . . . . . . . . . . . . . . . 619

27.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623

28 Monetary Policy in the New Keynesian Model 626

28.1 Policy in the Partial Sticky Price Model . . . . . . . . . . . . . . . . . . . . . . . 627

28.2 The Case for Price Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634

28.3 The Natural Rate of Interest and Monetary Policy . . . . . . . . . . . . . . . . . 639

28.4 The Taylor Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644

29 The Zero Lower Bound 647

29.1 The IS-LM-AD Curves with the ZLB . . . . . . . . . . . . . . . . . . . . . . . . . 649

29.2 Equilibrium Effects of Shocks with a Binding ZLB . . . . . . . . . . . . . . . . . 655

29.3 Why is the ZLB Costly? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 658

29.4 Fiscal Policy at the ZLB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663

29.5 How to Escape the ZLB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665

29.6 How to Avoid the ZLB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667

29.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 668

30 Open Economy Version of the New Keynesian Model 671

30.1 Deriving the AD Curve in the Open Economy . . . . . . . . . . . . . . . . . . . 672

30.2 Equilibrium in the Open Economy Model . . . . . . . . . . . . . . . . . . . . . . 674

30.3 Comparing the Open and Closed Economy Variants of the Model . . . . . . . . 675

30.3.1 Comparison in the Small Open Economy Version of the Model . . . . . 681

30.4 Effects of Foreign Shocks in the Open Economy New Keynesian Model . . . . 685

30.4.1 Increase in rFt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685

30.4.2 Increase in Qt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687

30.5 Fixed Exchange Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689

30.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696

17

VI Money, Credit, Banking, and Finance 698

31 The Basics of Banking 701

31.1 Asymmetric Information: Adverse Selection and Moral Hazard . . . . . . . . . 703

31.2 The Bank Balance Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 708

31.3 Managing the Balance Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711

31.3.1 Credit Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712

31.3.2 Liquidity Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714

31.4 Modern Banking and Shadow Banking . . . . . . . . . . . . . . . . . . . . . . . . 717

31.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723

32 The Money Creation Process 725

32.1 Some Definitions and Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725

32.2 Open Market Operations and the Simple Deposit Multiplier with T-Accounts 729

32.3 The Money Multiplier with Cash and Excess Reserve Holdings . . . . . . . . . 736

32.4 Two Monetary Episodes: The Great Depression and Great Recession . . . . . 749

32.4.1 Great Depression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 750

32.4.2 Great Recession . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753

32.4.3 Fractional Reserve Banking . . . . . . . . . . . . . . . . . . . . . . . . . . 757

32.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 758

33 A Model of Liquidity Transformation and Bank Runs 759

33.1 Model Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 759

33.2 Enter a Bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 761

33.3 Bank Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764

33.4 Policies to Deal with Bank Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . 768

33.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 771

34 Bond Pricing and the Risk and Term Structures of Interest Rates 773

34.1 Bond Cash Flow Repayment Plans . . . . . . . . . . . . . . . . . . . . . . . . . . 774

34.1.1 Yield to Maturity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775

34.2 Bond Pricing with No Uncertainty: A General Equilibrium Approach . . . . . 779

34.3 Default Risk and the Risk Structure of Interest Rates . . . . . . . . . . . . . . . 784

34.3.1 No Income Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 789

34.3.2 No Default Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 792

34.3.3 Income Risk and Default Risk . . . . . . . . . . . . . . . . . . . . . . . . . 794

34.4 Time to Maturity and the Term Structure of Interest Rates . . . . . . . . . . . 797

18

34.4.1 No Uncertainty: The Expectations Hypothesis . . . . . . . . . . . . . . . 800

34.4.2 Uncertainty and the Term Premium . . . . . . . . . . . . . . . . . . . . . 805

34.5 Conventional versus Unconventional Monetary Policy . . . . . . . . . . . . . . . 818

34.5.1 A Model with Short and Long Term Riskless Debt and Long Term

Risky Debt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 819

34.5.2 Conventional Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . 826

34.5.3 Unconventional Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 828

34.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 836

35 The Stock Market and Bubbles 838

35.1 Equity Pricing in a Two Period General Equilibrium Model . . . . . . . . . . . 840

35.2 Comparing Different Kinds of Stocks . . . . . . . . . . . . . . . . . . . . . . . . . 847

35.3 Moving Beyond Two Periods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 852

35.3.1 The Gordon Growth Model . . . . . . . . . . . . . . . . . . . . . . . . . . 862

35.4 Bubbles and the Role of the Terminal Condition . . . . . . . . . . . . . . . . . . 864

35.4.1 A Numerical Example with Bubbles . . . . . . . . . . . . . . . . . . . . . 867

35.4.2 Should Monetary Policy Attempt to Prick Bubbles? . . . . . . . . . . . 874

35.5 Equilibrium Stock Prices with Endogenous Production: the Neoclassical Model876

35.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 880

36 Financial Factors in a Macro Model 883

36.1 Incorporating an Exogenous Credit Spread . . . . . . . . . . . . . . . . . . . . . 884

36.2 Detailed Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 887

36.3 Equilibrium Effects of an Increase in the Credit Spread . . . . . . . . . . . . . . 890

36.4 The Financial Accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 892

36.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 900

37 Financial Crises and The Great Recession 902

37.1 Financial Crises: The Great Depression and Great Recession . . . . . . . . . . 902

37.2 The Great Recession: Some More Specifics on the Run . . . . . . . . . . . . . . 909

37.3 Thinking About the Great Recession in the AD-AS Model . . . . . . . . . . . . 916

37.4 Unconventional Policy Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923

37.4.1 Federal Reserve Lending . . . . . . . . . . . . . . . . . . . . . . . . . . . . 924

37.4.2 Fiscal Stimulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927

37.4.3 Unconventional Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . 930

37.5 Lingering Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 937

37.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 938

19

VII Appendices 962

A Mathematical Appendix 963

A.1 Variables and Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 963

A.2 Exponents and Logs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964

A.3 Summations and Discounted Summations . . . . . . . . . . . . . . . . . . . . . . 965

A.4 Growth Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 967

A.5 Systems of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 969

A.6 Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 970

A.7 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 976

B Probability and Statistics Appendix 986

B.1 Measures of Central Tendency: Mean, Median, Mode . . . . . . . . . . . . . . . 986

B.2 Expected Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 987

B.3 Measures of Dispersion: Variance and Standard Deviation . . . . . . . . . . . . 991

B.4 Measures of Association: Covariance and Correlation . . . . . . . . . . . . . . . 994

C The Neoclassical Model with an Upward-Sloping Y s Curve 998

C.1 The Neoclassical Model with an Intertemporal Dimension to Labor Supply . . 999

C.2 Effects of Shocks with Upward-Sloping Y s . . . . . . . . . . . . . . . . . . . . . . 1003

C.3 Sources of Output Fluctuations with an Upward-Sloping Y s Curve . . . . . . . 1007

D The New Keynesian Model with Sticky Wages 1009

D.1 Equilibrium Effects of Shocks in the Sticky Wage Model . . . . . . . . . . . . . 1014

D.1.1 Comparing the Sticky Wage Model to the Neoclassical Model . . . . . . 1024

D.2 Dynamics in the Sticky Wage Model . . . . . . . . . . . . . . . . . . . . . . . . . 1028

D.2.1 A Non-Optimal Short Run Equilibrium . . . . . . . . . . . . . . . . . . . 1028

D.2.2 Dynamic Responses to Shocks . . . . . . . . . . . . . . . . . . . . . . . . . 1030

E Replacing the LM Curve with the MP Curve 1038

E.1 The AD Curve when the MP Curve Replaces the LM Curve . . . . . . . . . . . 1038

E.2 The Modified Supply Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044

E.3 The IS-MP-AD-AS Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1046

E.3.1 The Effects of Shocks in the IS-MP-AD-AS Model . . . . . . . . . . . . 1048

20

Part I

Introduction

21

Part I serves as an introduction to the book and a review of materials from a principles

course. Chapter 1 reviews some basics concerning national income and product accounts

(NIPA), discusses the distinction between real and nominal variables and how to construct

an aggregate price index, and discusses different measures of labor market variables. Chapter

2 explains what an economic model is and why models are useful when thinking about the

economy, particularly at a high level of aggregation. Chapter 3 includes a brief discussion

of the history of macroeconomics. In so doing, it provides some context for how modern

macroeconomics as it is now practiced came to be.

22

Chapter 1

Macroeconomic Data

In this chapter we define some basic macroeconomic variables and statistics and go over

their construction as well as some of their properties. For those of you who took principles

of macroeconomics, this should be a refresher. We start by describing what is perhaps the

single most important economic indicator, GDP.

1.1 Calculating GDP

Gross domestic product (GDP) is the current dollar value of all final goods and services

that are produced within a country within a given period of time. “Goods” are physical

things that we consume (like a shirt) while “services” are things that we consume but which

are not necessarily tangible (like education). “Final” means that intermediate goods are

excluded from the calculation. For example, rubber is used to produce tires, which are used

to produce new cars. We do not count the rubber or the tires in used to construct a new car

in GDP, as these are not final goods – people do not use the tires independently of the new

car. The value of the tires is subsumed in the value of the newly produced car – counting

both the value of the tires and the value of the car would “double count” the tires, so we only

look at “final” goods.1 “Current” means that the goods are valued at their current period

market prices (more on this below in the discussion of the distinction between “real” and

“nominal”).

GDP is frequently used as a measure of the standard of living in an economy. There are

many obvious problems with using GDP as a measure of well-being – as defined, it does

not take into account movements in prices versus quantities (see below); the true value to

society of some goods or services may differ from their market prices; GDP does not measure

non-market activities, like meals cooked at home as opposed to meals served in a restaurant

(or things that are illegal); it does not say anything about the distribution of resources among

society; etc. Nevertheless, other measures of well-being have issues as well, so we will focus

1There are many nuances in the NIPA accounts, and this example is no exception. Tires included in theproduction of a new car are not counted in GDP because these are not final goods, but replacement tires soldat an auto shop for an already owned car are. More generally, depending on circumstances sometimes a goodis an intermediate good and other times it is a final good.

23

on GDP.

Let there be n total final goods and services in the economy – for example, cell phones (a

good), haircuts (a service), etc. Denote the quantities of each good (indexed by i) produced

in year t by yi,t for i = 1,2, . . . , n and prices by pi,t. GDP in year t is the sum of prices timesquantities:

GDPt = p1,ty1,t + p2,ty2,t + ⋅ ⋅ ⋅ + pn,tyn,t =n

∑i=1pi,tyi,t

As defined, GDP is a measure of total production in a given period (say a year). It must

also be equal to total income in a given period. The intuition for this is that the sale price of

a good must be distributed as income to the different factors of production that went into

producing that good – i.e. wages to labor, profits to entrepreneurship, interest to capital

(capital is some factor of production, or input, that itself has to be produced and is not used

up in the production process), etc. For example, suppose that an entrepreneur has a company

that uses workers and chain-saws to produce firewood. Suppose that the company produces

1000 logs at $1 per log; pays its workers $10 per hour and the workers work 50 hours; andpays $100 to the bank, from which it got a loan to purchase the chain-saw. Total paymentsto labor are $500, interest is $100, and the entrepreneur keeps the remaining $400 as profit.The logs contribute $1000 to GDP, $500 to wages, $100 to interest payments, and $400 toprofits, with $500 + $100 + $400 = $1,000.

The so-called “expenditure” approach to GDP measures GDP as the sum of consumption,

C; investment, I; government expenditure, G; and net exports, NX. Net exports is equal to

exports, X, minus imports, IM , where exports are defined as goods and services produced

domestically and sold abroad and imports are defined as goods and services produced abroad

and purchased domestically. Formally:

GDPt = Ct + It +Gt + (Xt − IMt) (1.1)

Loosely speaking, there are four broad actors in an aggregate economy: households, firms,

government (federal, state, and local), and the rest of the world. We measure aggregate

expenditure by adding up the spending on final goods and services by each of these actors.

Things that households purchase – food, gas, cars, etc. – count as consumption. Firms produce

stuff. Their expenditures on new capital, which is what is used to produce new goods (e.g. a

bulldozer to help build roads), is what we call investment. Government expenditures includes

everything the government spends either on buying goods (like courthouses, machine guns,

etc.) or on services (including, in particular, the services provided by government employees).

The latter half – basically counting government payments to workers as expenditure – is

making use of the fact that income = expenditure from above, as there is no other feasible

24

way to “value” some government activities (like providing defense). This number does not

include transfer payments (social security, Medicaid, etc.) and interest payments on debt

from the government (which together amount to a lot). The reason transfer payments do

not count in government expenditure is that these transfers do not, in and of themselves,

constitute expenditure on new goods and services. However, when a retiree takes her Social

Security payment and purchases groceries, or when a Medicaid recipient visits a doctor, those

expenditures get counted in GDP. Finally, we add in net exports (more on this in a minute).

In summary, what this identity says is that the value of everything produced, GDPt, must be

equal to the sum of the expenditure by the different actors in the economy. In other words,

the total value of production must equal the total value of expenditure. So we shall use the

words production, income, and expenditure interchangeably.

If we want to sum up expenditure to get the total value of production, why do we subtract

imports (IM in the notation above)? After all, GDP is a measure of production in a country

in a given period of time, while imports measure production from other countries. The reason

is because our notion of GDP is the value of goods and services produced within a country;

the expenditure categories of consumption, investment, and government spending do not

distinguish between goods and services that are produced domestically or abroad. So, for

example, suppose you purchase an imported Mercedes for $50,000. This causes C to go up,but should not affect GDP. Since this was produced somewhere else, IM goes up by exactly

$50,000, leaving GDP unaffected. Similarly, you could imagine a firm purchasing a Canadianmade bulldozer – I and IM would both go up in equal amounts, leaving GDP unaffected.

You could also imagine the government purchasing foreign-produced warplanes which would

move G and IM in offsetting and equal directions. As for exports, a Boeing plane produced

in Seattle but sold to Qatar would not show up in consumption, investment, or government

spending, but it will appear in net exports, as it should since it is a component of domestic

production.

There are a couple of other caveats that one needs to mention, both of which involve how

investment is calculated. In addition to business purchases of new capital (again, capital

is stuff used to produce stuff), investment also includes new residential construction and

inventory accumulation. New residential construction is new houses. Even though households

are purchasing the houses, we count this as investment. Why? At a fundamental level

investment is expenditure on stuff that helps you produce output in the future. A house is

just like that – you purchase a house today (a “stock”), and it provides a “flow” of benefits

for many years going forward into the future. There are many other goods that have a similar

feature – we call these “durable” goods – things like cars, televisions, appliances, etc. At some

level we ought to classify these as investment too, but for the purposes of national income

25

accounting, they count as consumption. From an economic perspective they are really more

like investment; it is the distinction between “firm” and “household” that leads us to put new

durable goods expenditures into consumption. However, even though residential homes are

purchased by households, new home construction is counted as a component of investment.

Inventory “investment” is the second slightly odd category. Inventory investment is the

accumulation (or dis-accumulation) of unsold, newly produced goods. For example, suppose

that a company produced a car in 1999 but did not sell it in that year. It needs to count in

1999 GDP since it was produced in 1999, but cannot count in 1999 consumption because

it has not been bought yet. Hence, we count it as investment in 1999, or more specifically

inventory investment. When the car is sold (say in 2000), consumption goes up, but GDP

should not go up. Here inventory investment would go down in exactly the same amount of

the increase in consumption, leaving GDP unaffected.

We now turn to looking at the data, over time, of GDP and its expenditure components.

Figure 1.1 plots the natural log of GDP across time. These data are quarterly and begin

in 1947.2 The data are also seasonally adjusted – unless otherwise noted, we want to look

at seasonally adjusted data when making comparisons across time. The reason for this is

that there are predictable, seasonal components to expenditure that would make comparisons

between quarters difficult (and would introduce some systematic “choppiness” into the plots

– download the data and see for yourself). For example, there are predictable spikes in

consumer spending around the holidays, or increases in residential investment in the warm

summer months.

When looking at aggregate series it is common to plot series in the natural log. This is

nice because, as you can see in Appendix A, it means that we can interpret differences in the

log across time as (approximately) percentage differences – reading off the vertical difference

between two points in time is approximately the percentage difference of the variable over

that period. For example, the natural log of real GDP increases from about 6.0 in 1955 to

about 6.5 in 1965; this difference of 0.5 in the natural logs means that GDP increased by

approximately 50 percent over this period. For reasons we will discuss more in detail below,

plotting GDP without making a “correction” for inflation makes the series look smoother

than the “real” series actually is. To the eye, one observes that GDP appeared to grow at a

faster rate in the 1970s than it did later in the 1980s and 1990s. This is at least partially

driven by higher inflation in the 1970s (again, more on this below).

2You can download the data for yourselves from the Bureau of Economic Analysis.

26

www.bea.gov

Figure 1.1: Logarithm of Nominal GDP

5

6

7

8

9

10

50 55 60 65 70 75 80 85 90 95 00 05 10 15

Figure 1.2 plots the components of GDP, expressed as shares of total GDP. We see

that consumption expenditures account for somewhere between 60-70 percent of total GDP,

making consumption by far the biggest component of aggregate spending. This series has

trended up a little bit over time; this upward trend is largely mirrored by a downward trend

in net exports. At the beginning of the post-war sample we exported more than we imported,

so that net exports were positive (but nevertheless still a small fraction of overall GDP). As

we’ve moved forward into the future net exports have trended down, so that we now import

more than we export. Investment is about 15 percent of total GDP. Even though this is a

small component, visually you can see that it appears quite volatile relative to the other

components. This is an important point to which we shall return later. Finally, government

spending has been fairly stable at around 20 percent of total GDP. The large increase very

early in the sample has to do with the Korean War and the start of the Cold War.

27

Figure 1.2: GDP Components as a Share of Total GDP

.58

.60

.62

.64

.66

.68

.70

50 55 60 65 70 75 80 85 90 95 00 05 10 15

Consumption/GDP

.12

.14

.16

.18

.20

.22

50 55 60 65 70 75 80 85 90 95 00 05 10 15

Investment/GDP

.14

.16

.18

.20

.22

.24

.26

50 55 60 65 70 75 80 85 90 95 00 05 10 15

Government/GDP

-.06

-.04

-.02

.00

.02

.04

.06

50 55 60 65 70 75 80 85 90 95 00 05 10 15

Net Exports/GDP

1.2 Real versus Nominal

Measured GDP could change either because prices or quantities change. Because we are

interested in the behavior of quantities (which is ultimately what matters for well-being), we

would like a measure of production (equivalent to income and expenditure) that removes the

influence of price changes over time. This is what we call real GDP.

Subject to the caveat of GDP calculation below, in principle real prices are denominated

in units of goods, whereas nominal prices are denominated in units of money. Money is

anything which serves as a unit of account. As we’ll see later in the book, money solves a

bartering problem and hence makes exchange much more efficient.

To make things clear, let’s take a very simple example. Suppose you only have one good,

call it y. People trade this good using money, call it M . We are going to set money to be the

numeraire: it serves as the “unit of account,” i.e. the units by which value is measured. Let

p be the price of goods relative to money – p tells you how many units of M you need to

buy one unit of y. So, if p = 1.50, it says that it takes 1.50 units of money (say dollars) tobuy a good. Suppose an economy produces 10 units of y, e.g. y = 10, and the price of goodsin terms of money is p = 1.50. This means that nominal output is 15 units of money (e.g.1.50 × 10, or p ⋅ y). It is nominal because it is denominated in units of M – it says how manyunits of M the quantity of y is worth. The real value is of course just y – that is the quantity

28

of goods, denominated in units of goods. To get the real from the nominal we just divide by

the price level:

Real = NominalPrice

= pyp

= y.

Ultimately, we are concerned with real variables, not nominal variables. What we get utility

from is how many apples we eat, not whether we denominate one apple as one dollar, 100

Uruguayan pesos, or 1.5 euros.

Going from nominal to real becomes a little more difficult when we go to a multi-good

world. You can immediately see why – if there are multiple goods, and real variables are

denominated in units of goods, which good should we use as the numeraire? Suppose you

have two goods, y1 and y2. Suppose that the price measured in units of money of the first

good is p1 and the price of good 2 is p2. The nominal quantity of goods is:

Nominal = p1y1 + p2y2.

Now, the real relative price between y1 and y2 is just the ratio of nominal prices, p1/p2.p1 is “dollars per unit of good 1” and p2 is “dollars per unit of good 2”, so the ratio of the

prices is “units of good 2 per units of good 1.” Formally:

p1p2

=$

good 1

$good 2

= good 2good 1

(1.2)

In other words, the price ratio tells you how many units of good 2 you can get with one

unit of good 1. For example, suppose the price of apples is $5 and the price of oranges is $1.The relative price is 5 – you can get five oranges by giving up one apple. You can, of course,

define the relative price the other way as 1/5 – you can buy 1/5 of an apple with one orange.We could define real output (or GDP) in one of two ways: in units of good 1 or units of

good 2:

Real1 = y1 +p2p1y2 (Units are good 1)

Real2 =p1p2y1 + y2 (Units are good 2).

As you can imagine, this might become a little unwieldy, particularly if there are many

goods. It would be like walking around saying that real GDP is 14 units of Diet Coke, or 6

29

cheeseburgers, if Diet Coke or cheeseburgers were used as the numeraire. As such, we have

adopted the convention that we use money as the numeraire and report GDP in nominal

terms as dollars of output (or euros or lira or whatever).

But that raises the issue of how to track changes in GDP across time. In the example

above, what if both p1 and p2 doubled between two periods, but y1 and y2 stayed the same?

Then nominal GDP would double as well, but we’d still have the same quantity of stuff.

Hence, we want a measure of GDP that can account for this, but which is still measured in

dollars (as opposed to units of one particular good). What we typically call “real” GDP in the

National Income and Products Accounts is what would more accurately be called “constant

dollar GDP.” Basically, one arbitrarily picks a year as a baseline. Then in subsequent years

one multiplies quantities by base year prices. If year t is the base year, then what we call real

GDP in year t + s is equal to the sum of quantities of stuff produced in year t + s weightedby the prices from year t. This differs from nominal GDP in that base year prices are used

instead of current year prices. Let Yt+s denote real GDP in year t+ s, s = 0, 1, 2, . . . . Let therebe n distinct goods produced. For quantities of goods y1,t+s, y2,t+s, . . . , yn,t+s, we have:

Yt = p1,ty1,t + p2,ty2,t + ⋅ ⋅ ⋅ + pn,tyn,tYt+1 = p1,ty1,t+1 + p2,ty2,t+1 + ⋅ ⋅ ⋅ + pn,tyn,t+1Yt+2 = p1,ty1,t+2 + p2,ty2,t+2 + ⋅ ⋅ ⋅ + pn,tyn,t+2.

Or, more generally, using the summation notation covered in Appendix A:

Yt+h =n

∑i=1pi,tyi,t+h for h = 0,1,2.

From this we can implicitly define a price index (an implicit price index) as the ratio of

nominal to real GDP in a given year:

Pt =p1,ty1,t + p2,ty2,t + ⋅ ⋅ ⋅ + pn,tyn,tp1,ty1,t + p2,ty2,t + ⋅ ⋅ ⋅ + pn,tyn,t

= 1

Pt+1 =p1,t+1y1,t+1 + p2,t+1y2,t+1 + ⋅ ⋅ ⋅ + pn,t+1yn,t+1p1,ty1,t+1 + p2,ty2,t+1 + ⋅ ⋅ ⋅ + pn,tyn,t+1

Pt+2 =p1,t+2y1,t+2 + p2,t+2y2,t+2 + ⋅ ⋅ ⋅ + pn,t+2yn,t+2p1,ty1,t+2 + p2,ty2,t+2 + ⋅ ⋅ ⋅ + pn,tyn,t+2

.

Or, more succinctly,

Pt+h =∑ni=1 pi,t+hyi,t+h∑ni=1 pi,tyi,t+h

for h = 0,1,2.

30

A couple of things are evident here. First, we have normalized real and nominal GDP to

be the same in the base year (which we are taking as year t). This also means that we are

normalizing the price level to be one in the base year (what you usually see presented in

national accounts is the price level multiplied by 100). Second, there is an identity here that

nominal GDP divided by the price level equals real GDP. If prices on average are rising, then

nominal GDP will go up faster than real GDP, so that the price level will rise.

A problem with this approach is that the choice of the base year is arbitrary. This matters

to the extent that the relative prices of goods vary over time. To see why this might be a

problem, let us consider a simple example. Suppose that an economy produces two goods:

haircuts and computers. In year t, let the price of haircuts be $5 and computers by $500,and there be 100 hair cuts and 10 computers produced. In year t + 1, suppose the price ofhaircuts is $10, but the price of computers is now $300. Suppose that there are still 100haircuts produced but now 20 computers. Nominal GDP in year t is $5,500, and in year t + 1it is $7,000. If one uses year t as the base year, then real GDP equals nominal in year t, andreal GDP in t + 1 is $10,500. Using year t as the base year, one would conclude that realGDP grew by about 91 percent from t to t + 1. What happens if we instead use year t + 1 asthe base year? Then real GDP in year t + 1 would be $7,000, and in year t real GDP wouldbe $4,000. One would conclude that real GDP grew between t and t+ 1 by 75 percent, whichis substantially different than the 91 percent one obtains when using t as the base year.

To deal with this issue, statisticians have come up with a solution that they call chain-

weighting. Essentially they calculate real GDP in any two consecutive years (say, 1989 and

1990) two different ways: once using 1989 as the base year, once using 1990 as the base year.

Then they calculate the growth rate of real GDP between the two years using both base years

and take the geometric average of the two growth rates. Chain-weighting is a technical detail

that we need not concern ourselves with much, but it does matter in practice, as relative

prices of goods have changed a lot over time. For example, computers are far cheaper in

relative terms now than they were 10 or 20 years ago.

Throughout the book we will be mainly dealing with models in which there is only

one good – we’ll often refer to it as fruit, but it could be anything. Fruit is a particularly

convenient example for reasons which will become evident later in the book. This is obviously

an abstraction, but it’s a useful one. With just one good, real GDP is just the amount of

that good produced. Hence, as a practical matter we won’t be returning to these issues of

how to measure real GDP in a multi-good world.

Figure 1.3 below plots the log of real GDP across time in the left panel. Though

considerably less smooth than the plot of log nominal GDP in Figure 1.1, the feature that

sticks out most from this figure is the trend growth – you can approximate log real GDP

31

pretty well across time with a straight line, which, since we are looking at the natural log,

means roughly constant trend growth across time. We refer to this straight line as a “trend.”

This is meant to capture the long term behavior of the series. The average growth rate

(log first difference) of quarterly nominal GDP from 1947-2016 was 0.016, or 1.6 percent.

This translates into an annualized rate (what is most often reported) of about 6 percent

(approximately 1.6 × 4). The average growth rate of real GDP, in contrast, is significantlylower at about 0.008, or 0.8 percent per quarter, translating into about 3.2 percent at an

annualized rate. From the identities above, we know that nominal GDP is equal to the price

level times real GDP. As the growth rate of a product is approximately equal to the sum

of the growth rates, growth in nominal GDP should approximately equal growth in prices

(inflation) plus growth in real GDP.

Figure 1.3: Real GDP

7.5

8.0

8.5

9.0

9.5

10.0

50 55 60 65 70 75 80 85 90 95 00 05 10 15

Real GDPTrend

Log real GDP and its trend

-.20

-.15

-.10

-.05

.00

.05

.10

50 55 60 65 70 75 80 85 90 95 00 05 10 15

Detrended real GDP

Figure 1.4 plots the log GDP deflator and inflation (the growth rate or log first difference

of the GDP deflator) in the right panel. On average inflation has been about 0.008, or

0.8 percent per quarter, which itself translates to about 3 percent per year. Note that

0.008 + 0.008 = 0.016, so the identity appears to work. Put differently, about half of thegrowth in nominal GDP is coming from prices, and half is coming from increases in real

output. It is worth pointing out that there has been substantial heterogeneity across time in

the behavior of inflation – inflation was quite high and volatile in the 1970s but has been

fairly low and stable since then.

32

Figure 1.4: GDP Deflator

0

20

40

60

80

100

120

50 55 60 65 70 75 80 85 90 95 00 05 10 15

GDP Deflator

-.01

.00

.01

.02

.03

.04

50 55 60 65 70 75 80 85 90 95 00 05 10 15

Inflation - GDP Deflator

Turning our focus back to the real GDP graph, note that the blips are very minor in

comparison to the trend growth. The right panel plots “detrended” real GDP, which is

defined as actual log real GDP minus its trend. In other words, detrended GDP is what is left

over after we subtract the trend from the actual real GDP series. The vertical gray shaded

areas are “recessions” as defined by the National Bureau of Economic Research. There is

no formal definition of a recession, but loosely speaking they define a recession as two or

more quarters of a sustained slowdown in overall economic activity. For most of the recession

periods, in the left plot we can see GDP declining if we look hard enough. But even in the

most recent recession (official dates 2007Q4–2009Q2), the decline is fairly small in relation to

the impressive trend growth. You can see the “blips” much more clearly in the right plot.

During most of the observed recessions, real GDP falls by about 5 percentage points (i.e.

0.05 log points) relative to trend. The most recent recession really stands out in this respect,

where we see GDP falling by more than 10 percent relative to trend.

A final thing to mention before moving on is that at least part of the increase in real

GDP over time is due to population growth. With more people working, it is natural that we

will produce more products and services. The question from a welfare perspective is whether

there are more goods and services per person. For this reason, it is also quite common to

look at “per capita” measures, which are series divided by the total population. Population

growth has been pretty smooth over time. Since the end of WW2 it has averaged about